An addition (15x15) was added to my house in Fairfax, VA by the previous owners, which is not part of the central air/cooling system. As the house is on concrete slap, it appears untenable to add new duct work.

What is the best option for heating/cooling the room? Is a mini-split heat pump the correct path or will it be overkill (9K BTU seems to large for the room)? Can I get away with an electric baseboard for winter and allow the central air to cool the room in summer?

Are their better options?